In this section we review the theory of characteristic classes of representations of a finite group \(G\) . Our reference is [1]}.
Associated to complex representations \(\pi \)  of \(G\)  are cohomology classes \(c_i(\pi ) \in H^{2i}(G,\mathbb {Z})\) , for \(0 \le i \le \deg \pi \) , called Chern classes.
We have \(c_0(\pi )=1\) . The first Chern class, applied to linear characters, gives an isomorphism
\(c_1: \mathrm {Hom}(G,S^1) \overset{\sim }{\rightarrow } H^2(G,\mathbb {Z}).\) 
